Actuators based on unbalanced moments of inertia

ABSTRACT

Methods and computer-readable mediums are provide that, in some embodiments maximize bending of an actuator and, in other embodiments, minimize bending of the actuator. For example, in one embodiment, a method is provided that acquires a first ratio of a modulus of inertia for a first component to a Young&#39;s Modulus for the first component. The method also acquires a second ratio of a modulus of inertia for a second component to a Young&#39;s Modulus for the second component. Thereafter, the method provides an actuator (which includes the first component and second component). The actuator has a cross-sectional shape such that the first ratio substantially equal to said second ratio. In various embodiments of the invention, the actuator is spun fibers formed into batting and used as insulation, or may form an active element of a thermostat.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of under 35 U.S.C. §119(e) of U.S.Provisional Patent Application No. 61/563,040, filed Nov. 23, 2011,which application is incorporated herein by reference in its entirety.

BACKGROUND

1. Field of the Invention

Embodiments of the present invention generally relate to actuators andmore specifically to tailoring the moments of inertia of at least twocomponents, of the actuator, to enhance or suppress bending.

2. Description of the Related Art

It has long been known that two sheets of metal with differentcoefficients of thermal expansion (“CTE”) will bend with changes intemperature. The traditional approach to this technology is illuminatedby the “bi-metallic spring.” The general relationship for when the twometals (i.e., in a bi-metallic strip) are of the same thickness isanalyzed in Timoshenko, S., Analysis of Bi-metal Thermostats, J. Opt.Soc. Am. (1925), 11(2), pp. 233-255 (hereinafter “Timoshenko”).

Timoshenko analyzed the bending of a bi-metal thermostat of rectangularcross-section and concluded:

-   -   The curvature is proportional to the difference in elongation of        the two metals and inversely proportional to the thickness of        the strip. It is seen that the magnitude of the ratio [of the        Young's moduli of the two metals] does not produce any        substantial effect on the curvature of the strip. See Timoshenko        at page 235.

A bi-metallic strip 100 is provided in FIG. 1. Specifically, thebi-metallic strip 100 includes a first component 102 and a secondcomponent 104. The first component 102 is made of a different metal thanthe second component 104. The first component 102 and second component104 have the same dimensions and different coefficients of linearexpansion and moments of inertia. Heating the bi-metallic strip 100causes bending of the bi-metallic strip 100.

Equations are provided below for calculating the temperature ofbuckling, the complete travel during buckling, and the temperature ofbuckling in a backward direction. By using these equations, thedimensions of the bi-metallic strip 100 for a given temperature ofoperation and a given complete range of temperature can be calculated.It has long been known that two sheets of metal with differentcoefficients of thermal expansion (“CTE”) will bend with changes intemperature. The general relationship for the two metals (i.e.,components 102 and 104) are of the same thickness (as provided byTimoshenko) is provided by Equation 1:

$\begin{matrix}{\frac{1}{\rho} = \frac{24( {\alpha_{2} - \alpha_{1}} )( {\Delta\; T} )}{h( {14 + n + \frac{1}{n}} )}} & {{Equation}\mspace{14mu}(1)}\end{matrix}$

where the CTEs of the two materials are α₁ (component 102) and α₂(component 104), the change in temperature is ΔT, h is the combinedthickness of components 102 and 104, n is the ratio of the mechanicalmoduli of components 102 and 104, the radius of curvature is ρ, and the“curvature” is 1/ρ.

Note that Equation (1) can alternatively be expressed as Equation (2)below.

$\begin{matrix}{\frac{1}{\rho_{rect}} = \frac{6( {\alpha_{2} - \alpha_{1}} )( {t - t_{0}} )( {1 + m} )^{2}}{h\lbrack {{3( {1 + m} )^{2}} + {( {1 + {n\; m}} )( {m^{2} + \frac{1}{n\; m}} )}} \rbrack}} & {{Equation}\mspace{14mu}(2)}\end{matrix}$

where

$\frac{1}{\rho_{rect}}$is the radius of curvature of the strip 100, h is the height or diameterof the fiber, α₂ is the coefficient of thermal expansion for component104, α₁ is the coefficient of thermal expansion for component 102, n isthe ratio of the Young's moduli of the components 102 and 104, and m isa ratio of the thickness of components 102 and 104. Note that settingm=1 in Equation (2) yields Equation (1).

According to the analysis in Timoshenko, the bending of the bonded metalsheets (i.e., components 102 and 104 combined) is not a strong functionof the mechanical modulus of the component metals. E₁ and E₂ are theelastic moduli of components 102 and 104, respectively. It is seen thatthe magnitude of

$n = \frac{E_{1}}{E_{2}}$does not produce any substantial effect on the curvature of the strip.For example, when n=1, then Equation (1) above is reduced to Equation(3).

$\begin{matrix}{\frac{1}{\rho} = \frac{3( {\alpha_{2} - \alpha_{1}} )( {\Delta\; T} )}{2h}} & {{Equation}\mspace{14mu}(3)}\end{matrix}$

where the CTEs of the two materials are α₁ (component 102) and α₂(component 104), the change in temperature is ΔT, h is the combinedthickness of components 102 and 104, the radius of curvature is ρ, andthe “curvature” is 1/ρ.

Similarly, when n=½ or n=2 then Equation (1) is reduced to Equation (4)below.

$\begin{matrix}{\frac{1}{\rho} = \frac{48( {\alpha_{2} - \alpha_{1}} )( {\Delta\; T} )}{33h}} & {{Equation}\mspace{14mu}(4)}\end{matrix}$

where the CTEs of the two materials are α₁ (component 102) and α₂(component 104), the change in temperature is ΔT, h is the combinedthickness of components 102 and 104, the radius of curvature is ρ, andthe “curvature” is 1/ρ.

“For a ratio of Young's moduli of 2, the “difference . . . [incurvature] is only about 3 percent.” See Timoshenko at page 236.

However, many combinations of materials that could be useful havemechanical moduli which can vary by a factor or ten or more. Based onthese same equations the bending would be reduced by about one third. Ifthe mechanical moduli differ by two orders of magnitude the bending isreduced to only 15% of the amount of bending that would be seen in thecase where mechanical moduli are equal.

Examples of materials with very different mechanical moduli are polymersabove and below their glass transition temperatures. Amorphous polymersabove their glass transition temperature (i.e., in a rubbery state)usually have much higher CTEs than those below their glass transitiontemperature (i.e., in a glassy state) and would make good candidates forbending in response to temperature changes to act as a thermostat or atemperature adaptive insulation. Unfortunately, a decrease in modulus ofabout 3 orders of magnitude occurs at the glass transition making thiscombination of materials essentially useless.

Many materials of current technological interest such as gels, amorphousmetals, shape memory polymers, and nanocomposites have mechanical moduliwhich vary by orders of magnitude limiting the combinations of materialsthat can be used.

However, for polymeric materials, the elastic modulus can change bythree orders of magnitude below and above the glass transitiontemperature (Aklonis and McKnight, 1983). It is just such a combinationof a polymer above its glass transition temperature and one below itsglass transition temperature (or in a crystalline form) that gives thegreatest difference in coefficients of thermal expansion.

The prior art (e.g., U.S. Pat. No. 4,115,620 issued Sep. 19, 1978)discloses an even polymer blend (i.e., extruded at 50:50 ratio).

Although U.S. Pat. No. 4,315,881 (issued Feb. 16, 1982) discloses thatthe ratio by weight of extruded fiber components is 30:70 to 70:30 and40:60 to 60:40.

Generally, the prior art does not use the moments of inertia of thecomponents to determine the ratio of those components (in an extrudedmaterial) and manipulate the shape of the extruded material to maximizebending.

Thus there is a need to use a wider selection of materials ofsignificantly different mechanical moduli. There is also a need totailor the moments of inertia of at least two components, in anactuator, to enhance or suppress bending.

SUMMARY

To the knowledge of the present inventors, the prior art does not adjustthe ratio of two components to optimize bending. Further, the prior artdoes not appear to use or manipulated these ranges to optimize bendingof extruded material.

Embodiments of the present invention generally relate to actuators andmore specifically to tailoring the moments of inertia of at least twocomponents, of the actuator, to enhance or suppress bending.

For example, in one embodiment, a method is provided that acquires afirst ratio of a modulus of inertia for a first component to a Young'sModulus for the first component. The method also acquires a second ratioof a modulus of inertia for a second component to a Young's Modulus forthe second component. Thereafter, the method provides an actuator (whichincludes the first component and second component). The actuator has across-sectional shape such that the first ratio is substantially equalto said second ratio.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the presentinvention can be understood in detail, a more particular description ofthe invention, briefly summarized above, may be had by reference toembodiments, some of which are illustrated in the appended drawings. Itis to be noted, however, that the appended drawings illustrate onlytypical embodiments of this invention and are therefore not to beconsidered limiting of its scope, for the invention may admit to otherequally effective embodiments.

FIG. 1 depicts a bi-metal spring in accordance with the prior art;

FIG. 2 depicts a first embodiment of the invention;

FIG. 3 depicts a second embodiment of the invention;

FIG. 4 depicts a graph of the temperature response (i.e., curvature)using a polymer having a rectangular shaped cross-section;

FIG. 5 depicts a graph of the temperature response for a polymer havinga circular cross-section in accordance with embodiments of theinvention;

FIG. 6 depicts a graph of the temperature response for a systematicallyvaried area fraction of the base of the triangle in accordance withembodiments of the invention;

FIG. 7 depicts a triangular cross-section of a fiber in accordance withembodiments of the invention;

FIG. 8 depicts a plot of a temperature response for an exemplarycross-section of an actuator in accordance with embodiments of theinvention:

FIG. 9 depicts an embodiment of a method in accordance with embodimentsof the invention;

FIG. 10 depicts an embodiment of a high-level block diagram of ageneral-purpose computer architecture for providing an actuator inaccordance with embodiments of the invention; and

FIG. 11 depicts an embodiment of a system in accordance with embodimentsof the invention.

To facilitate understanding, similar reference numerals have been used,wherever possible, to designate identical elements that are common tothe figures.

DETAILED DESCRIPTION

In the following description, numerous specific details are set forth toprovide a more thorough understanding of the invention. As will beapparent to those skilled in the art, however, various changes usingdifferent configurations may be made without departing from the scope ofthe invention. In other instances, well-known features have not beendescribed in order to avoid obscuring the invention. Thus, the inventionis not considered limited to the particular illustrative embodimentsshown in the specification and all such alternate embodiments areintended to be included in the scope of the appended claims.

In short, embodiments of the invention make the ratio of the moment ofinertia to the Young's Moduli for a first component equal to the ratioof the moment of inertia to the Young's Moduli for a second component.One way to make the two ratios equal is to provide a shape (i.e., theratio) for the combination of the two components such that there is lessof one component than the other component. Exemplary shapes are providedin FIGS. 2 and 3. It is to be understood that the shapes provided hereinare for illustrative purposes only and not intended to limit the scopeof the invention (i.e., limit the invention to the exemplary shapes).

Some of the commercial applications of embodiments of the inventioninclude, but are not limited to, temperature adaptive insulation,stimuli responsive textiles, self-tightening sutures andswitches/thermostats.

For illustrative purposes only, aspects of the invention are describedherein as maximizing the bending of the actuators. However, thesedescriptions are not intended to limit the invention in any way. Forexample, aspects of the invention also include limiting the bending ofthe actuators.

For illustrative purposes only, aspects of the invention are describedherein using polymers. However, these descriptions are not intended inany way to limit the scope of the invention nor are they intended tolimit the scope of the materials which can be used.

One application of the invention is an adaptive thermal insulation forclothing and equipment that provides greater insulation at lowtemperatures and less at high temperatures. Clothing that adapts tochanges in environmental conditions means that fewer items will berequired to effectively protect soldiers or civilians over a wide rangeof operating temperatures.

For illustrative purposes only, embodiments of the invention aredescribed herein with respect to temperature adaptive insulation. Forexample, soldiers must adapt their clothing to a wide variety of weatherand climate conditions. This often means adding or subtracting garmentsand providing more or less ventilation by using openings in theclothing. The insulation required for thermal balance can change rapidlyespecially in mountainous regions as soldiers move from one altitude toanother or encounter climatic variables. If the insulation level is toolow it may result in hypothermia or frostbite leading to degradedperformance (loss of dexterity and fine motor control). If theinsulation level is too high it can result in unnecessary sweating whichcollects within the insulation, degrading the insulation and increaseswater consumption, which in turn may lead to dehydration.

Although the term “extrusion” is used herein that use is forillustrative purposes only and not intended, in any way, to limit thescope of the invention. For example, in various embodiments, compoundsare bonded, secured, attached, or coupled to each other.

In aspects of the invention, moments of inertia of the components aretailored such that the response of materials with very differentmechanical moduli is accommodated. As an example, one implementation ofthis is a bi-component fiber of triangular cross section (depicted inFIG. 2). In FIG. 2, a first component 202 is depicted as the “top” ofthe triangular shaped extrusion 200 while the second component 204 isthe “bottom” of the triangular shaped extrusion 200 (note that thesecond component 204 has a trapezoidal shape).

Experimentally it is found that considerably greater bending can be seenin configurations with the first component 202 composed of a highermodulus material than the second compound 204 (rather than a reverseconfiguration with the second compound 204 on top).

FIG. 2 also depicts a length (“b”) of one dimension 206 of firstcomponent 202 and a length (“c”) of one dimension 208 of secondcomponent 204. First component 202 and second component 204 includeheights α₁₁ and α₂₂, respectively. The curvature for triangular crosssection 200 is provided in Equation (5), as follows:

$\frac{1}{\rho_{tri}} = \frac{18( {\alpha_{2} - \alpha_{1}} )( {t - t_{0}} )( {1 + m} )^{2}}{\begin{matrix}{h\{ {{9( {1 + m} )^{2}} + {2{( {1 + m} )\lbrack {{( {m^{2} + 1} )( {1 - a_{1}} )} + \frac{2( {a_{1} - a_{1}^{2}} )}{( {a_{1} + 1} )^{2}} +} }}} } \\  \;{{m^{3}\frac{( {a_{1} - a_{1}^{2}} )}{( {a_{1} + 1} )}} + {\frac{1}{n}\frac{( {a_{1}^{2} + {4a_{1}} + 1} )( {1 - a_{1}} )}{m( {a_{1}^{2} + a_{1}} )}}} \rbrack \}\end{matrix}}$where

$\frac{1}{\rho_{tri}}$is the radius of curvature of the triangular cross-section 200, h is thetotal height or diameter of the components 202 and 204, α₂ is thecoefficient of thermal expansion for component 204, α₁ is thecoefficient of thermal expansion for component 202, n is the ratio ofthe Young's moduli of the components 202 and 204, m is a ratio of thethickness of components 202 and 204, α₁ is the height of the component202, and α₂ is the height of component 204. Note that α₁+α₂=1 and thatα₂=1−α₁ has been substituted into Equation (5).

Calculation of the moment of inertia for first component 202 is providedby Equation (6).

$\begin{matrix}{I_{1} = \frac{a_{11}^{3}b}{36}} & {{Equation}\mspace{14mu}(6)}\end{matrix}$

where I₁ is the moment of inertia for first component 202, α₁₁ is theheight of the first component 202, and b is the length of one of thedimensions (i.e., the base) of the first component 202.

Calculation of the moment of inertia for the second component 204 isprovided by Equation (7).

$\begin{matrix}{I_{2} = \frac{a_{22}^{3}( {b^{2} + {4{bc}} + c^{2}} )}{36( {b + c} )}} & {{Equation}\mspace{14mu}(7)}\end{matrix}$

where I₂ is the moment of inertia for second component 204, α₂₂ is theheight of the second component 204, and b and c are lengths of the upperand lower sides (of the trapezoid) of the second component 204.

Equation (7) is simplified to Equation (8) when m=1.

$\begin{matrix}{\frac{1}{\rho_{tri}} = \frac{72( {\alpha_{2} - \alpha_{1}} )( {t - t_{0}} )}{h\lbrack {41 + {\frac{2}{3}n} + {\frac{26}{3}\frac{1}{n}}} \rbrack}} & {{Equation}\mspace{14mu}(8)}\end{matrix}$

where

$\frac{1}{\rho_{tri}}$is the radius of curvature of the triangular shaped extrusion 200, h isthe total height of the triangular shaped extrusion 200, α₂ is thecoefficient of thermal expansion for component 204, α₁ is thecoefficient of thermal expansion for component 202, n is the ratio ofthe Young's moduli of the components 202 and 204.

FIG. 3 depicts another embodiment 300 of the invention. Specifically,FIG. 3 depicts a substantially circular shaped cross-section 300. Thesubstantially circular shaped cross-section 300 includes a firstcomponent 302 (at an upper portion of the cross-section 300) and asecond component 304 (at a lower portion of the cross-section 300).

The first component 302 includes a height 308 (α₁) and a dimensionallength 306 (b). The second component 304 includes a height 310 (α₂₂).Extrusion 300 includes a diameter 314 (depicted in dashed lined). Angleθ 312 is taken from the diameter 314 (and center of cross-section 300)and is the angle formed between the diameter 314 and dashed lines 316extending from the center of the extrusion 300 to the ends ofdimensional length 306.

The curvature for circular shaped cross-section 300 is provided below inEquation (9), (10), (11), and (12) (when components 302 and 304 are ofunequal height).

$\begin{matrix}{X = \frac{( {\theta - {\sin\;\theta}} )}{2}} & {{Equation}\mspace{14mu}(9)}\end{matrix}$

where X is used as a substitution to simplify Equation (12).

$\begin{matrix}{F = {\pi - \frac{( {\theta - {\sin\;\theta}} )}{2}}} & {{Equation}\mspace{14mu}(10)}\end{matrix}$

where F is used as a substitution to simplify Equation (12).

$\begin{matrix}{k = \frac{A_{1}}{A_{2}}} & {{Equation}\mspace{14mu}(11)}\end{matrix}$

where A₁ represents the cross-sectional area of the first component 302and A₂ represents the cross-sectional area of the second component 304.

$\begin{matrix}{\frac{1}{\rho_{circ}} = \frac{2\;{{XF}( {\alpha_{2} - \alpha_{1}} )}( {t - t_{0}} )( {1 + m} )^{2}}{h\{ {{XF} + {\lbrack {{n( {{BX} - C} )} + {k( {{BF} - C} )}} \rbrack( \frac{1}{{nk} + 1} )}} \}}} & {{Equation}\mspace{14mu}(12)}\end{matrix}$

where

$\frac{1}{\rho_{circ}}$is the radius of curvature of the circular cross-section 300, h is thetotal height or diameter of the circular cross-section 300, α₂ is thecoefficient of thermal expansion for component 304, α₁ is thecoefficient of thermal expansion for component 302, n is the ratio ofthe Young's moduli of the components 302 and 304, m is a ratio of thethickness of components 302 and 304, X is provided by Equation (9), F isprovided by Equation (10), k is the ratio of cross-sectional areas ofthe first component 302 to the second component 304, and B and C arefunctions of the geometry of the circle and are used as a substitute forvariables to simply Equation (12).

Equation (12) can be simplified to Equation (13) when m=1.

$\begin{matrix}{\frac{1}{\rho_{circ}} = \frac{\frac{\pi}{2}( {\alpha_{2} - \alpha_{1}} )( {t - t_{0}} )}{h\lbrack {( {\frac{\pi^{2}}{8} - \frac{8}{9}} ) + {( {\frac{\pi^{2}}{16} - \frac{4}{9}} )n} + {( {\frac{\pi^{2}}{16} - \frac{4}{9}} )\frac{1}{n}}} \rbrack}} & {{Equation}\mspace{14mu}(13)}\end{matrix}$

where

$\frac{1}{\rho_{circ}}$is the radius of curvature of the circular cross-section 300, h is thetotal height or diameter of the circular cross-section 300, α₂ is thecoefficient of thermal expansion for component 304, α₁ is thecoefficient of thermal expansion for component 302, n is the ratio ofthe Young's moduli of the components 302 and 304, and m is a ratio ofthe thickness of components 302 and 304.

Embodiments of the invention use the ratio of the moment of inertia tothe Young's Moduli for a first component equal to the ratio of themoment of inertia to the Young's Moduli for a second component to createshaped fibers that bend in response to temperature. The shaped fibersare multi-component fibers (e.g., bi-component or tri-component fibers).Multi-component spinning can be used as a cost effective way ofproducing large quantities of fibers that bend as the temperaturechanges.

One way to use such fibers is to create a loose mat or batting. Battingsare commonly used as insulation in, for example, jackets and sleepingbags. In various embodiments, the polymeric fibers (e.g., bi-componentor tri-component polymeric fibers having circular or triangularcross-sections) are used to provide insulation which changes thicknessin response to temperature. The polymeric fibers have at least twocomponents with different coefficients of thermal expansion (CTE). Asthe temperature changes, polymeric fibers are temperature responsive andcurl as the temperature is decreased. Curling of the polymeric fibers(in response to the decrease temperature) causes the insulationthickness to increase providing greater thermal insulation.

As indicated above, bi-component and tri-component fibers can be spunfrom commercially available polymers of widely differing coefficients ofthermal expansion. Some combination of polymers and fiber geometryresults in changes of more than two orders of magnitude (>1.5×10⁻² per °C.).

Fibers can be spun to create a temperature adaptive thermal insulationusing a tri-component fiber extruder. One of the purposes of a thirdcomponent (depicted in FIG. 7) is to limit the interfacial shear betweenthe high and low CTE components.

In some embodiments of the invention, thickness changes by more than1.5% per ° C. (30% over a temperature range from approximately 20° C. to0° C.).

FIG. 4 depicts a plot 400 of the temperature response (i.e., curvature)using Equation (1). Specifically, graph 400 includes a curvature 402(parallel to a “Z axis”), a ratio of moduli

$( \frac{E_{1}}{E_{2}} )$404 (parallel to a “Y axis”), and an upper rectangle height fraction 406(parallel to an “X axis”). The graph 400 depicts plot 408 which showsthat when the ratio of the moduli are equal to 1 then the optimumbending occurs at 50% of each component. The maximum bending at anyratio of the moduli 404 from 0.1-10 is different depending upon thecomposition of the fiber.

FIG. 5 shows a graph 500 of the temperature response for a series whenthe area fraction of the base of the triangle is systematically varied.Specifically, graph 500 includes a curvature 402 (parallel to a “Zaxis”), a ratio of moduli

$( \frac{E_{1}}{E_{2}} )$404 (parallel to a “Y axis”), and an upper segment height fraction 504(parallel to an “X axis”). The graph 500 depicts plot 502 which showsthat when compared to a rectangular cross-section (e.g., in the plot408), a circular cross-section provides a potential for greater bendingof the fiber (in various embodiments) and greater suppression of bendingof the fiber (in other embodiments). In addition, plot 502 also showsthat the components used can be at a higher ratio of the moduli thantaught in the prior art.

FIG. 6 depicts a graph 600 of the temperature response for asystematically varied area fraction of the base of the triangle inaccordance with embodiments of the invention. Specifically, graph 600includes a curvature 402 (parallel to a “Z axis”), a ratio of moduli

$( \frac{E_{1}}{E_{2}} )$404 (parallel to a “Y axis”), and an upper triangle height fraction 604(parallel to an “X axis”). The graph 600 depicts plot 602 which showsthat when compared to a rectangular cross-section (e.g., in the plot408) a triangular shaped cross-section provides a potential for greaterbending of the fiber (in various embodiments) and greater suppression ofbending of the fiber (in other embodiments). In addition, plot 602 alsoshows that the components used can be at a higher ratio of the modulithan taught in the prior art.

It appears from plot 604 that the batting response is greater fordecreasing area fraction of the bottom section (i.e., second component204) of a triangular shaped cross-section of a fiber. The results areconsistent with the analytical model. Some fiber samples show a changein the thickness of 1.8% per ° C. while the lowest response is about0.3% or less. In some embodiments, an area fraction of 0.3 is theapproximate lower limit for the fiber spinning apparatus. Plot 604indicates an optimum response at a level that is a function of the ratioof the mechanical moduli of the components in a two component system.

In various embodiments of the invention, isotactic and syndiotacticpolypropylene (i-PP, s-PP) are the components used in the fibers. Theisotactic polymer is of a relatively high crystallinity and has arelatively high modulus and low coefficient of thermal expansion. Incontrast, the syndiotactic polymer crystallizes slowly and is expectedto have a high CTE and a low modulus.

Values for polypropylene can be taken from Uehara, H., Yamazaki, Y. andKanamoto, T. Tensile Properties of Highly Syndiotactic Polypropylene.1996, Vol. 37, 1, pp. 57-64 (hereinafter “Uehara”) for calculation andcomparison of values obtained during testing. For example, drawnisotactic polypropylene presumed to have a fiber modulus of 20 GPa whilewell drawn syndiotactic polypropylene had a fiber modulus of 3 GPa—aratio of 6.67- to-1. A typical CTE for an amorphous polymer is around10⁻⁴ m/m ° C. Crystalline and highly oriented polymeric fibers can havea negative CTE along the length of the fiber. The chain axis CTE forisotactic PP crystals is negative, −1×10⁻⁵ m/m ° C. [7].

In various embodiments of the invention, fibers are spun from commercialgrades of polypropylene. In various embodiments, spun fibers have anedge length of approximately about 50 microns. In various embodiments,fibers are spun with a draw ratio of about 2.5-to-1 and collected ontorolls of about 15 cm diameter. Crystalline and highly oriented polymericfibers can have a negative CTE along the length of the fiber. The chainaxis CTE for isotactic PP crystals is negative, −1×10⁻⁵ m/m ° C.

In various embodiments, the CTE and modulus in the fiber direction ofeach component is a function of the level of crystallinity and theorientation of the crystal, amorphous and intermediate phases.

FIG. 7 depicts a triangular cross-section of a fiber 700 in accordancewith embodiments of the invention. The fiber 700 includes a firstcomponent 702, a center section 704, and a second component 706.

In various embodiments, the first component 702 is s-PP, the secondcomponent 706 is i-PP, and the center section 704 includes a smallamount of dye added to a random ethylene propylene copolymer (co-EP)with a low modulus to limit interfacial stress between the firstcomponent 702 and the second component 706 but with a coefficient ofthermal expansion similar to s-PP.

In various embodiments, a high modulus polymer of the second component706 provides a modulus ratio of 1/6.67 or 0.15. From the equations above(e.g., Equations (5), (6), (7), and (8)), for a system with this modulusratio, the maximum curvature is predicted to occur when the fraction ofthe first component 702 is between about 0.8 and about 0.85 (secondcomponent fraction between about 0.2 and about 0.15). A micrograph 708of actual fibers is also depicted in FIG. 7. “Table 2” below providesexamples of fibers (e.g., Fiber 1) and component ratios.

TABLE 2 polymer/area fraction of each polymer Fiber A (s-PP) B (co-EP) C(i-PP) 1 0.5 0.2 0.3 2 0.45 0.2 0.35 3 0.40 0.20 0.40 4 0.35 0.20 0.45 50.30 0.20 0.50

Fibers cut from rolls spontaneously curled to form batting. The curlingis the result of relaxation of stresses from the spinning process andthe change in length as the fibers are cooled from the spinningtemperature.

The battings can then be die cut into samples for testing (e.g., cutinto about 20 in² (129 cm²) circular samples). The thickness of thesamples can be measured in a temperature controlled chamber bycompressing the samples with a pressure of about 0.02 psi. The thicknessof the samples can first be measured at room temperature then in anenvironmental chamber cooled to zero ° C.

FIG. 8 depicts a plot 800 of a temperature response for an exemplarycross-section of an actuator in accordance with embodiments of theinvention. Specifically, FIG. 8 shows the change in thickness of battingper ° C. 802 (parallel to the “Y-axis”) where the area fraction of thebase of the triangle 804 (parallel to the “X-axis”) is systematicallyvaried. The results are consistent with the analytical model. Forexample, FIG. 8 depicts a change in thickness of 1.8% per degree C.while the lowest response is about 0.3% or less. An area fraction ofabout 0.3 is the approximate lower limit for the fiber spinningapparatus.

An analysis of the thermally-induced curvature of bi-component fibers ofvarious cross-sections with respect to the ratio of the moduli of thecomponents and the fraction of the cross-section that each componentoccupies is provided. Graphical analysis of these functions supportsqualitatively that to achieve maximum curvature of the fibers, thedesign space of interest resides along the “spine” of the surfaces.Quantitatively, the functions allow the proportions of the components tobe selected to maximize the fiber curvature for a given pair ofpolymers. Experimental fibers of varying component fractions are spun,formed into mats and their thickness measured at various temperatures.The experimentally measured thickness changes are in good agreement withthe analytical results for fiber bending. Based on a one dimensionalheat transfer model the change in thickness appears to be sufficient fora practical adaptive thermal insulation.

FIG. 9 depicts an embodiment of a method 900 in accordance withembodiments of the invention. The method 900 begins at step 902 andproceeds to step 904.

At step 904, a ratio (i.e., “Ratio1”) is determined between the momentof inertia and the Young's modulus for a first component. Thereafter,the method 900 proceeds to step 906.

At step 906, a ratio (i.e., “Ratio2”) is determined between the momentof inertia and the Young's modulus for a second component. Thereafter,the method 900 proceeds to step 908.

At step 908, an actuator is formed (e.g., spun fibers or adhesion) usingthe first component and the second component. The amounts of the firstcomponent and the second component that are used are determined byRatio1 and Ratio2. The amount of each component is adjusted until theratios I/E (of each component) are the same. So that Ratio1 and Ratio2are substantially equal, the actuators can have non-rectangular shapes(i.e., shapes where the dimensions of the first component are not equalto the dimensions of the second component) (e.g., triangular orcircular). After formation of the actuators, the method 900 proceeds toand ends at step 912.

In various embodiments, the method 900 proceeds to optional step 910. Atoptional step 910 the actuators (when the actuators are spun fibers) areformed into batting. After optional step 910, the method proceeds to andends at step 912.

FIG. 10 depicts an embodiment of a high-level block diagram of ageneral-purpose computer architecture 1000 for an actuator in accordancewith embodiments of the invention. For example, the general-purposecomputer 1000 is suitable for use in performing the method of FIG. 9.The general-purpose computer of FIG. 10 includes a processor 1010 aswell as a memory 1004 for storing control programs and the like. Invarious embodiments, memory 1004 also includes programs (e.g., depictedas an “actuator cross-section” 1012 for creating actuators having across-sectional shape such that a ratio of the moment of inertia toYoung's modulus for a first component is substantially equal to themoment of inertia to Young's modulus for a second component) forperforming the methods and for producing the embodiments describedherein. The processor 1010 cooperates with conventional supportcircuitry 1008 such as power supplies, clock circuits, cache memory andthe like as well as circuits that assist in executing the softwareroutines 1006 stored in the memory 1004. As such, it is contemplatedthat some of the process steps discussed herein as software processescan be loaded from a storage device (e.g., an optical drive, floppydrive, disk drive, etc.) and implemented within the memory 1004 andoperated by the processor 1010. Thus, various steps and methods of thepresent invention can be stored on a computer readable medium. Thegeneral-purpose computer 1000 also contains input-output circuitry 1002that forms an interface between the various functional elementscommunicating with the general-purpose computer 1000.

Although FIG. 10 depicts a general-purpose computer 1000 that isprogrammed to perform various control functions in accordance with thepresent invention, the term computer is not limited to just thoseintegrated circuits referred to in the art as computers, but broadlyrefers to computers, processors, microcontrollers, microcomputers,programmable logic controllers, application specific integratedcircuits, and other programmable circuits, and these terms are usedinterchangeably herein. In addition, although one general-purposecomputer 1000 is depicted, that depiction is for brevity only. It isappreciated that each of the methods described herein can be utilized inseparate computers.

FIG. 11 depicts an embodiment of a system 1100 in accordance withembodiments of the invention.

The system 1100 includes an extruder 1102 ₁ and extruder 1102 ₂. Each ofthe extruders 1102 ₁ and 1102 ₂ are adapted to receive a differentcomponent (e.g., one polymer is poured into extruder 1102 ₁ and adifferent polymer is poured into extruder 1102 ₂). Illustratively, thepolymer poured into extruder 1102 ₁ is one of isotactic polypropylene, apolyethyleneterephthalate (PET) and polyester; and the polymer poured inextruder 1102 ₂ is one of an amorphous polymer, a syndiotacticpolypropylene, and a polycarbonate. After polymers are poured into theextruders 11021 and 11022, the extruders 11021 and 11022 melt thepolymers.

After the polymers melt, the extruders 1102 ₁ and 1102 ₂ force thepolymers through metering pumps 1104 ₁ and 1104 ₂. Each metering pumps1104 ₁ and 1104 ₂ regulate the amount of melted polymer that passesthrough the metering pump 1104 ₁ and 1104 ₂ to a dye 1106. A ratio of amodulus of inertia to a Young's Modulus for each component(illustratively referred to hereinafter as the “first ratio” and “secondratio” respectively) is acquired. The metering pumps 1104 ₁ and 1104 ₂regulate the amount of each polymer that passes through the dye 1106.The dye 1106 has an internal periphery which shapes and combines the twopolymers. The metering pumps 1104 ₁ and 1104 ₂ regulate the amount ofpolymer passing through each respective pump such that the amountextruded through the dye 1106 results in the first ratio beingsubstantially equal to the second ratio. In addition, the internalperiphery (of the dye 1106) forces an actuator (not shown) (i.e., acombination of the two polymers) passing through the dye 1106 to havethe internal periphery of the dye 1106. The resulting actuator has across-sectional shape (e.g., a triangular cross-section or asubstantially circular cross-section) where the first ratio issubstantially equal to said second ratio.

After an actuator is formed (i.e., as fibers), the fibers are spun ontocylindrical drum 1108 ₁. In various embodiments, the system 1100includes multiple cylindrical drums 1108 ₁, 1108 ₂, . . . and 1108 _(n).

Illustratively, FIG. 11 depicts a bi-component extruder. However, thatdepiction is not intended in any way to limit the scope of theinvention. For example, embodiments of the invention can be used inconjunction with tri-component extruders.

In various embodiments of the invention can be utilized withMicro-Electro-Mechanical-Systems (“MEMS”). Embodiments of the inventioncan be used to design/build actuators by machining, Computer NumericalControlled machining (“CNC”), and micromachining processes. Even at themicron or nanometer level aspects of the invention can be used to makean actuator.

As used herein, the terms “having,” “containing,” “including,”“comprising” and the like are open ended terms that indicate thepresence of stated elements or features, but do not preclude additionalelements or features. The articles “a,” “an,” and “the” are intended toinclude the plural as well as the singular, unless the context clearlyindicates otherwise. The term “acquiring” is an open ended term that canmean any way of obtaining the characteristics, including measuring,looking up in a handbook, checking with a manufacture of material,estimating from theoretical calculations, and/or a physical measurement.

While the foregoing is directed to embodiments of the present invention,other and further embodiments of the invention may be devised withoutdeparting from the basic scope thereof, and the scope thereof isdetermined by the claims that follow.

We claim:
 1. A method for configuring an actuator to bend apredetermined amount for a change in ambient conditions, comprising:determining a desired amount of bending for an actuator based on ambientconditions; selecting a first component having a first ratio of amodulus of inertia to a Young's Modulus for said first component;selecting a second component having a second ratio of a modulus ofinertia to a Young's Modulus for said second component; and combiningsaid first component with said second component to form the actuatorwherein said actuator includes a cross-sectional shape having said firstratio substantially equal to said second ratio; and whereby the actuatoris configured to bend the desired amount for a change in ambientconditions.
 2. The method of claim 1 wherein said combining comprisesone of extruding, machining, spinning, adhering, and cross-linking ofsaid first component and said second component.
 3. The method of claim 1wherein said actuator is a spun fiber.
 4. The method of claim 3 furthercomprising forming a batting from said spun fiber.
 5. The method ofclaim 1 wherein said cross-sectional shape is one of a triangularcross-section and a substantially circular cross-section.
 6. The methodof claim 1 further comprising forming said actuator into one of asuture, a batting, a thermostat needle, and a gel.
 7. A method formaking an actuator that is configured to bend a predetermined amount fora change in ambient conditions, comprising: determining a desired amountof bending for an actuator based on ambient conditions; selecting afirst polymer for injecting through a dye, wherein said first polymerhas a first coefficient of thermal expansion (CTE), and a first ratio ofa modulus of inertia to a Young's Modulus, and selecting a secondpolymer for injecting, simultaneously to said injection of said firstpolymer, through said dye, wherein said second polymer has a second CTEhigher than said first CTE, and a second ratio of a modulus of inertiato a Young's Modulus; and extruding the actuator from said dye, whereinsaid actuator includes a cross-sectional shape having said first ratiosubstantially equal to said second ratio and whereby the actuator isconfigured to bend the desired amount for a change in ambientconditions.
 8. The method of claim 7 further comprising forming saidactuator into one of one of a suture, a batting, and a gel.
 9. Themethod of claim 7 wherein said first polymer is one of an isotacticpolypropylene, a polyethyleneterephthalate (PET) and polyester.
 10. Themethod of claim 7 wherein said second polymer is one of an amorphouspolymer, a syndiotactic polypropylene, and a polycarbonate.
 11. Themethod of claim 7 wherein said dye has one of a triangularcross-sectional shape and a substantially circular cross-sectionalshape.
 12. The method of claim 7 wherein said actuator is a spun fiberwith a draw ratio of about 2.5 to about 4.5.